% very simple model

x = (0:4)'; 
Y = [-1 0 0 0 1]';

n = length(Y);

X = [ones(n,1) x]; 

szX = size(X);
p = szX(2);   % total number of beta's

betahat = (X' * X)^(-1) * X' * Y;
Yhat = X * betahat;    % predicted values 
resid = Y - Yhat;
SSE = sum(resid.^2)
SST = sum(( Y - mean(Y)).^2);
s2 = SSE/(n-p)
R2 = (SST-SSE)/SST

plot(x,Y,'.')
 hold on
plot(x, Yhat, '*')
 hold off
 
 
  
 
   R2adj = 1 - (n-1)/(n-p)*(1-R2)

  % now "saturated" polynomial: the one that would fit exactly all the pts 
 
   X = [ones(n,1) x x.^2 x.^3 x.^4]; 

szX = size(X);
p = szX(2);   % total number of beta's

betahat = (X' * X)^(-1) * X' * Y;